Receptor Children is a generic term for observation subjects who were gathered to become vessels for Finé's soul.
The biggest weak point of Finé's reincarnation system is that those who hold her seal carved into their genes must be exposed to an aufwachen waveform, it's the only point of the system that is left up to an overwhelming amount of simple chance. Regardless of the fact that her vessels can inherit her paranormal powers and memories, if they are not in an environment where those abilities can revive, then idle time simply passes. Thus, in order to overcome the weakness and prepare an "insurance," Finé began the project with the American government's F.I.S. If she lost the use of her current vessel in the middle of her plans, she wanted to assure she could revive without losing any time and restart her ambitions. Thus the receptor children were her attempt to prepare her next vessel ahead of time.
By searching through hospital records and personal information she isolated potential candidates, particularly those with thin ties to society, for example "those with no living relatives" (and in particular "infants and children). Above all, Japan had the highest amount of potential receptor children, and the reason for that is in about 722 BC a branch of a family in the Middle East that held the seal of Finé entered into ancient Japan.
The number of observation subjects that F.I.S. kept contained broke more than 1,000 people, however at the time of Finé's death they were unable to determine if she had been newly revived in one of them. At that point there were plans to dispose of the project entirely behind closed doors, but due to an uprising led by Nastassja and others, the existence of the Receptor Children and their confinement was brought to light and in fear of criticism from the international community the US Government quickly changed their tune.
Currently the subjects have been rescued and released of their own will or provided shelter.